Regularization, sparse recovery, and median-of-means tournaments

By Gábor Lugosi, Shahar Mendelson. 2017

51 citations recorded by the source corpus.

A regularized risk minimization procedure for regression function estimation is introduced that achieves near optimal accuracy and confidence under general conditions, including heavy-tailed predictor and response variables. The procedure is based on median-of-means tournaments, introduced by the authors in [8]. It is shown that the new procedure outperforms standard regularized empirical risk minimization procedures such as lasso or slope in heavy-tailed problems.

Subfields: Control and Systems Engineering, Management Science and Operations Research, Statistics and Probability

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In Control and Systems Engineering

In Management Science and Operations Research

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Citations in the corpus

Robust Aggregation for Federated Learning (2019, methodology): “Robust median-of-means were introduced in [70], with follow ups in [39, 53, 60, 61, 67].”
Convergence rates of least squares regression estimators with heavy-tailed errors (2017, background): “−1 2 + 1 2p . Constructing estimators other than the LSE that give rise to exponential tail bound under a heavy-tailed regression setting is also of signiﬁcant interest. We refer the readers to, e.g. [24, 45, 47] and references therein for this line of research. 3.2. Lower bound for the convergence ”